Concept explainers
Repeat Prob. 14-55E, ignoring all minor losses. How important are the minor losses in this problem? Discuss.
Whether the minor losses are important or not.
Answer to Problem 57EP
The minor losses are important because the volume flow rate is increased by
Explanation of Solution
Given Information:
Inner diameter of the duct is
Expression for steady energy equation from point 1 in the stagnant air region to point 2 at the duct outlet.
Here, the required head for the fan is
Expression for the total head loss.
Here, the velocity of the air is
Expression for Reynolds's number.
Here, the kinematic viscosity is
Expression for relative roughness.
Here, the roughness of the pipe is
Expression for the friction factor.
Expression for the volume flow rate.
Here, the area of the pipe is
Expression for the area of the pipe.
Substitute
.
Expression to convert the shutoff head from inches of water column to inches of air column.
Here, the density of the water is
Expression to convert the
Expression for the total head loss.
Here, the velocity of the air is
Calculation:
Refer to the Table-A-9E, "Properties of air at 1 atm pressure" to obtain the density of the air as
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Since at the operating point the available head and the required head are equal, therefore equate Equation (XIII) and (XIV).
Solve Equation (XIII) and Equation (XV) to obtain the value of velocity as
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Since at the operating point the available head and the required head are equal, therefore equate equation (XVI) and (XVIII).
Solve Equation (XVII) and Equation (XIX) to obtain the value of velocity as
Substitute
Therefore, the volume flow rate when considering the minor losses is
Conclusion:
The minor losses are important because the volume flow rate is increased by
Want to see more full solutions like this?
Chapter 14 Solutions
FLUID MECHANICS CONNECT ACCESS
- The old Hydraulics laboratory in Mechanical Engineering used a roof tank tosupply apparatus with water at a nearly constant head. The water wascollected in an under floor sump, and then pumped back to the roof tankafter the experiment. The flow rate was 10 litre s-1. The tank was 6m abovethe sump, and the length of the pipe route was 15 m. The old 6” pipes arenow heavily corroded (k = 7.5 mm). The old pump has been scrapped. Whathead ΔH would be specified for a pump to restore the system using the oldpipes? What would the pump power be? If the pipes were replaced with 150mm diameter PVC pipes, what pump ΔH would be required?arrow_forwardIn an hydroelectric plant, 100 m^3/s of water flows from elevation of 120 m to a turbine, where electric power is generated. The overall efficiency of the turbine-generator is 80 percent Disregarding frictional losses in piping. Estimate the electric power output of this plant.arrow_forwardA reservoir supplies water through 100 m of 30-cm-diameter cast iron pipe to a turbine that extracts 80 hp from the flow. Given that Δz = 30 m. The water then exhausts to the atmosphere. Neglect minor losses. For water at 20°C, take ρ = 998 kg/m3 and μ = 0.001 kg/m-s. Take π = 22/7. In determining the flow rate of the given flow, two solutions are obtained. Are both the solutions valid? Yes or no?arrow_forward
- Justify your answer for each part  QUESTION : By considering a system divided into two identical subsystems determine if the quantity lnV +lnP −lnU is intensive, extensive, or the classification does not apply??arrow_forwardAn 8 cm diameter hydraulic cylinder has a 4 cm diameter rod. If the cylinder receives flow at 100 LPM and 12 MPa, find the extension and retraction speeds and extension and retraction load carrying capacities.arrow_forwardIn a hydroelectric power plant, water at 20°C is supplied to the turbine at a rate of 0.55 m3/s through a 200-m-long, 0.35-m-diameter cast iron pipe. The elevation difference between the free surface of the reservoir and the turbine discharge is 140 m, and the combined turbine–generator efficiency is 85 percent. Disregarding the minor losses because of the large length-to-diameter ratio, determine the electric power output of this plant.arrow_forward
- How long should a pipe with a diameter of 10 cm and a friction coefficient of 0.02 be, to be equivalent to another pipe 100 meters long, with the same diameter and roughness but with a sum of singular losses of 2?arrow_forwardkindly answer only number 5 1 is just a reference 1. A water from Agno River is pumped using a submerged pump at an efficiency of 78% that is discharged to a swimming pool in Itogon which has a free surface of 30 m above the Agno River water level. The pipe that was used has a diameter of 7 cm on the suction line and 5 cm on the discharge line from the pump. If the power requirement of the pump is 5 kW assuming that the elevation difference between the pump inlet and outlet and the effect of the kinetic energy correction factors are negligible, calculate for the followinga) Power requirement by the pump in kW b) Pressure difference across the pumpc) Pumping cost/day(24 hour) if the electricity cost is ₱2.00/kW-h 5. In reference to problem number 1, if another pump was used having a power requirement of 12 hP with an efficiency of 73% in pumping the water at 1.2 ft3/s through a constant diameter of a pipe. Determine the irreversible head loss of the piping system in ft of water if…arrow_forwardinclude a free body diagram Seawater is to be pumped into a large tank at a rate of 165 kg/min. The tank is opwn to atmostsphere and the water enters the tank from a 80 m height. The overall efficiency of the motor pump unit is 75 percent and the motor consumes electricity at a rate of 3.2 KW. If the irreversible headloss in the piping is 7 m, the velocity of the water (in m/s) at the tank inlet isA. 6.21B. 7.12C. 8.7D. 5.05arrow_forward
- Pls. answer thank you! A pelton type turbine was installed 31m below the head gate of the penstock. The head loss due to friction is 15% of the given elevation. The length of the penstock is 80 m and the coefficient of friction is 0.00093 (Morse). Determine the diameter in meters of the penstock and the power output in KW.arrow_forwardWater at 60 deg. F is pumped from a reservoir to the top of a mountain through a 6-in SCH 120 pipe at an average velocity of 12 ft/s. The pipe discharges into the atmosphere at a level 3000 ft above the level in the reservoir. The pipeline itself is 4500 ft. long. If the overall efficiency of the pump and the motor driving it is 70% and the cost of electric energy to the motor is 4 cents per kilowatt-hour,1. what is the hourly energy cost for pumping this water? $3.21$ 18.32$12.83$81.23$ 32.18$23.81none of the givenarrow_forwardA 40 mm diameter shaft is made of steel 50C4 (Sut 660 N/mm²) and has machined surface. The expected reliability is 99%. The theoretical stress concentration factor for the shape of the shaft is 1.6 and the notch sensitivity factor is 0.9. Determine the endurance limit of the shaft.arrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY